On This Page

Criss Cross Poker

Introduction

Photo taken at 2014 Global Gaming Expo.

Criss Cross Poker is poker variation by . In 2014, I started to hear reports of the game in several casinos in the eastern United States. The thrust of the game is the player bets on two hands, in part using five community cards placed in a cross pattern.

Rules

Play begins with the player making Ante Across and Ante Down bets of equal size. The player may also make an optional Five Card Bonus Bet.

The dealer gives the player two hole cards and places five community cards face down in a cross pattern.

The player may make an Across Bet, based on the Across Hand, equal to 1x to 3x the Ante Across bet, or fold.

The dealer will reveal the two outside cards on the horizontal row of the cross.

The player may make a Down bet, based on the Down Hand, equal to 1x to 3x the Ante Down bet, or fold.

The dealer will reveal the two outside cards on the vertical column of the cross.

The player may make a Middle Bet of 1x to 3x either Ante bet or fold.

The dealer will reveal the middle card.

The player uses his two hole cards and the three cards on the horizontal row of the cross to form the Across Hand.

Likewise, the player uses his two hole cards and the three cards on the vertical column of the cross to form the Down Hand.

The Middle Bet pays according to the higher ranking of the Across and Down hands.

All bets pay according to the pay table below. Wins are expressed on a "to one" basis.

Criss Cross Poker Pay Table

Hand

AnteBets Pay

Across, Down &Middle Bets Pay

Royal flush

1

500

Straight flush

1

100

Four of a kind

1

40

Full house

1

12

Flush

1

8

Straight

1

5

Three of a kind

1

3

Two pair

1

2

High pair (J-A)

1

1

Low pair (6-10)

0

0

All other

-1

-1

The Five Card Bonus bet pays according to the five community cards in the cross pattern and following pay table.

Five Card Bonus Bet Pay Table

Hand

Pays

Royal flush

250

Straight flush

100

Four of a kind

40

Full house

15

Flush

10

Straight

6

Three of a kind

4

Two pair

3

Sixes or better

1

Loser

-1

Analysis

Between two sets of possible hands, four combinations of raise bets, and folding at various stages of the game, there are 975 possible outcomes. I indicate the probability of all of them in my Criss Cross Poker Full Expected Value Table. However, I don't want to scare you off with that gigantic table here. Instead, I summarize the outcome of each hand below.

The following table shows the possible outcome of both the Ante Across and Across bets. The "pays" column shows the combined win between the two bets. The lower right cell shows that the player can expect to lose 0.600581 units between the two bets.

Ante Across and Across Bets

Hand

Across Bet

Pays

Combinations

Probability

Return

Royal flush

3

1501

12,972

0.000000

0.000231

Royal flush

1

501

116,748

0.000001

0.000694

Straight flush

3

301

25,944

0.000000

0.000093

Straight flush

1

101

1,141,536

0.000014

0.001368

Four of a kind

3

121

12,167,736

0.000144

0.017468

Four of a kind

1

41

7,601,592

0.000090

0.003698

Full house

3

37

48,800,664

0.000579

0.021423

Full house

1

13

68,414,328

0.000812

0.010552

Flush

3

25

2,101,464

0.000025

0.000623

Flush

1

9

163,550,976

0.001940

0.017464

Straight

3

16

2,451,708

0.000029

0.000465

Straight

1

6

288,484,308

0.003423

0.020537

Three of a kind

3

10

538,234,224

0.006386

0.063859

Three of a kind

1

4

1,170,645,168

0.013889

0.055557

Two pair

3

7

811,632,096

0.009630

0.067408

Two pair

1

3

3,010,230,432

0.035715

0.107146

High pair

3

4

1,170,593,280

0.013889

0.055555

High pair

1

2

9,458,722,620

0.112224

0.224448

Medium pair

3

0

1,385,409,600

0.016437

0.000000

Medium pair

1

0

11,610,887,160

0.137759

0.000000

Loser

3

-4

1,240,719,912

0.014721

-0.058883

Loser

1

-2

44,512,795,932

0.528127

-1.056254

Fold one unit

0

-1

4,576,521,600

0.054299

-0.054299

Fold two units

0

-2

4,203,010,800

0.049867

-0.099734

Fold four units

0

-4

0

0.000000

0.000000

Total

84,284,272,800

1.000000

-0.600581

The following table shows the possible outcome of both the Ante Down and Down bets. The "pays" column shows the combined win between the two bets. The lower right cell shows that the player can expect to lose 0.597666 units on the two bets combined.

Ante Down and Down Bets

Hand

Down Bet

Pays

Combinations

Probability

Return

Royal flush

3

1501

45,792

0.000001

0.000815

Royal flush

1

501

83,928

0.000001

0.000499

Straight flush

3

301

37,116

0.000000

0.000133

Straight flush

1

101

1,118,700

0.000013

0.001341

Four of a kind

3

121

12,233,808

0.000145

0.017563

Four of a kind

1

41

7,485,048

0.000089

0.003641

Full house

3

37

48,603,888

0.000577

0.021337

Full house

1

13

68,156,856

0.000809

0.010513

Flush

3

25

6,951,456

0.000082

0.002062

Flush

1

9

157,641,288

0.001870

0.016833

Straight

3

16

4,780,980

0.000057

0.000908

Straight

1

6

285,297,516

0.003385

0.020310

Three of a kind

3

10

540,593,136

0.006414

0.064139

Three of a kind

1

4

1,160,967,816

0.013774

0.055098

Two pair

3

7

814,576,176

0.009665

0.067652

Two pair

1

3

2,988,662,184

0.035459

0.106378

High pair

3

4

1,336,724,496

0.015860

0.063439

High pair

1

2

9,281,584,656

0.110122

0.220245

Medium pair

3

0

1,417,841,568

0.016822

0.000000

Medium pair

1

0

11,550,329,616

0.137040

0.000000

Loser

3

-4

1,450,469,088

0.017209

-0.068837

Loser

1

-2

44,370,555,288

0.526439

-1.052879

Fold one unit

0

-1

5,013,003,456

0.059477

-0.059477

Fold two units

0

-2

3,766,528,944

0.044688

-0.089377

Fold four units

0

-4

0

0.000000

0.000000

Total

84,284,272,800

1.000000

-0.597666

The following table shows the possible outcome of Middle bet. The lower right cell shows that the player can expect to win 1.111675 units on this bet.

Middle Bet

Hand

Middle Bet

Pays

Combinations

Probability

Return

Royal flush

3

1500

259,440

0.000003

0.004617

Royal flush

1

500

0

0.000000

0.000000

Straight flush

3

300

2,323,104

0.000028

0.008269

Straight flush

1

100

0

0.000000

0.000000

Four of a kind

3

120

39,488,184

0.000469

0.056221

Four of a kind

1

40

0

0.000000

0.000000

Full house

3

36

231,865,848

0.002751

0.099036

Full house

1

12

0

0.000000

0.000000

Flush

3

24

325,921,056

0.003867

0.092806

Flush

1

8

0

0.000000

0.000000

Straight

3

15

375,011,412

0.004449

0.066740

Straight

1

5

199,154,268

0.002363

0.011814

Three of a kind

3

9

2,751,292,188

0.032643

0.293787

Three of a kind

1

3

399,927,564

0.004745

0.014235

Two pair

3

6

5,494,091,328

0.065185

0.391111

Two pair

1

2

1,329,787,368

0.015777

0.031555

High pair

3

3

11,485,872,240

0.136275

0.408826

High pair

1

1

4,170,202,716

0.049478

0.049478

Medium pair

3

0

12,309,204,636

0.146044

0.000000

Medium pair

1

0

4,837,617,228

0.057396

0.000000

Loser

3

-3

1,789,381,740

0.021230

-0.063691

Loser

1

-1

29,763,340,080

0.353130

-0.353130

Fold

0

0

8,779,532,400

0.104166

0.000000

Total

84,284,272,800

1.000000

1.111675

The next table summarizes the expected win of all three groups of bets.

Summary

Bet(s)

Expected Win

Ante Across & Across

-0.600581

Ante Down & Down

-0.597666

Middle

1.111675

Total

-0.086571

The lower right cell shows an expected loss of 0.086571 units. Since the player must wager two units at least, I divided that by two to get a house edge of 4.33%.

Considering the raise bets, the average total bet by the end of the hand is 5.86529 units. Thus the element of risk, which is the ratio of expected loss to the total amount wagered, is 8.6571/5.8629 = 1.48%, which isn't bad for a poker variant game.

The standard deviation, relative to the combined initial wager, is 4.802.

Strategy

With all decision points, the only viable options are fold, minimum 1x raise, or maximum 3x raise. Never raise anything between 1x and 3x.

Across Strategy

If the hole cards are unsuited, unpaired, and the largest one is five or less, then fold.

If the hole cards are suited J/Q or any pair, then make the large raise.

With all other hole cards, make the small raise.

Down Strategy

This is a very similar decision to raising on the Across hand. However, the player has the benefit of seeing two extra cards. This can help in borderline situations. I have not implicitly identified these deviations from the Across strategy. However, I can say that knowing them, whatever they are, will increase the expected return by 0.29% the amount of the Ante Down bet, or lower the house edge by 0.15%.

Middle Strategy

With four cards seen, there are thousands of possible situations in terms of a Middle bet strategy. However, a perfect decision can be made by averaging the win over all possible 46 cards left in the deck under both a small and large Middle bet. I can say that if the player made either 3x bet, then he shouldn't fold. I can also say that 4.5% of the time the player will make both a small Across and Down bet and then fold the Middle bet.

Five Card Bonus Bet

The following table presents the possible outcomes of the Five Card Bonus Bet. The lower right cell shows a house edge of 3.53%, which for a side bet isn't bad.

Five Card Bonus Bet

Hand

Pays

Combinations

Probability

Return

Royal flush

250

4

0.000002

0.000385

Straight flush

100

36

0.000014

0.001385

Four of a kind

40

624

0.000240

0.009604

Full house

15

3,744

0.001441

0.021609

Flush

10

5,108

0.001965

0.019654

Straight

6

10,200

0.003925

0.023548

Three of a kind

4

54,912

0.021128

0.084514

Two pair

3

123,552

0.047539

0.142617

Sixes or better

1

760,320

0.292548

0.292548

Loser

-1

1,640,460

0.631199

-0.631199

Total

2,598,960

1.000000

-0.035336

Methodology

The game was analyzed by me in C++ by looping through all combin(52,2)*combin(50,2)*combin(48,2)*46 = 84,284,272,800 possible combinations. The program is about 600 lines of code and takes about six hours to run.